Well, let me unpack this for you. For millennia, the most important part of the home was the fireplace where the home is heated and food is cooked. Nowadays, there is some demon-possessed machine in the basement that does the heating job and our fireplaces are primarily decorative - but those are only recent "improvements". The house (edifice) was literally built up around the fireplace or hearth. And Pa Ingalls vividly demonstrated that family is built up (edified) there at the core of the home - the fireplace or hearth.
Ready for this? The Latin word for hearth is eides - clearly growing up from our ancient root ai. There where the burning happens, the core of the edifice is formed and family members are edified. It's all true.